The present invention relates to discrete-time or digital filters. Even more particularly, the present invention relates to a time-reversed infinite impulse response digital filter device and method, wherein time-domain asymmetric signal can be filtered by the time-reversed infinite impulse response filter so as to generate a time-domain symmetric: signal or signal having linear phase, in response thereto.
In a receive signal path, e.g., in a cellular telephone, a digital filter, or discrete-time filter, can be utilized to filter a received signal and to implement a response desired for further processing of the received signal, e.g., in a digital signal processor. Unfortunately, before the received signal is filtered by the discrete-time filter, the received signal is typically filtered by an analog filter in order to band-limit the received signal by filtering out undesirable frequency bands, e.g., frequency bands other than a desired cellular frequency band, such as adjacent cellular frequency bands. Problematically, the analog filter distorts the received signal, and generates a time-domain asymmetric signal.
As used herein, the term time-domain asymmetric signal, refers to a signal that is the output signal of an asymmetric electrical circuit. The asymmetric electrical circuit is a circuit that, in response to an electrical impulse or delta function, generates an output signal, i.e., impulse response, that is not symmetric about any point in time. Typically the impulse response has more energy following its time domain peak than proceeding it. In other words, the impulse response builds more quickly than it decays. For example, the impulse response may be an oscillating signal that is generated in response to the electrical impulse, and that dissipates (or decays) over time. As a result, the oscillating signal has a time-domain energy distribution wherein very little energy is distributed before its peak, and a greater amount of energy is distributed after its peak. This type of energy distribution can also be described as lacking linear phase.
Because analog filters are infinite impulse response filters, they are one type of asymmetric electrical circuit. Thus, the output signal generated by the analog filter, mentioned above, is referred to herein as the "asymmetric" signal, i.e., a signal that has been asymmetrically distorted by the analog filter.
Two types of discrete-time, or digital, filters are characterized based on their response to an electrical impulse, or delta function: finite impulse response filters (or FIR filters) and infinite impulse response filters (or IIR filters). The infinite impulse response filter exhibits asymmetric distortion (or lack of linear phase) similar to that of the analog filter described above. Because the IIR filter tends to asymmetrically distort the asymmetric signal, described above, and therefore tends to compound the asymmetric distortion caused by the analog filter, the IIR filter has, heretofore, not been a preferred filter for use in the cellular telephone receive signal path, where a symmetric output signal (i.e., an output signal free from asymmetric distortion, or having linear phase) is desired.
In theory, the FIR filter, however, can be designed to completely restore the distortions made by the analog filter, i.e., can be designed to generate a symmetric signal in response to the asymmetric signal. Problematically, in order to achieve this design an infinite number of unit delays and "taps" must be utilized, and an infinite amount of time is needed for an output signal, completely free from distortion, to be generated. Thus, as a practical matter, the FIR filter cannot completely restore the distortions made by the analog filter.
Instead, FIR filters used in receive signal paths where a symmetric output signal is desired are typically designed to restore the distortions made by the analog filter to within a prescribed tolerance. As a result, the FIR filter can be designed with, e.g., eight unit delays and sixteen "taps" which is considered reasonable for, e.g., the processing of cellular telephone signals. Additional delays and taps may be utilized to increase the symmetry of the FIR filter's impulse response.
Improved or complete restoration of the distortions introduced by the analog filter, without the need for additional delays and taps, is however very desirable.
Thus, improvements are needed in the filtering of electrical signals so as to, e.g., restore distortions introduced into the electrical signal by an asymmetric electrical circuit, such as an analog filter.